The uncertainties in the velocities of two particles,$A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times that of the mass of $A$. What is the ratio of uncertainties $\frac{\Delta x_A}{\Delta x_B}$ in their positions?

If you are driving a car of mass $1050 \, kg$ at a speed of $90 \, km/h$ and the uncertainty in the velocity of the car is $1 \, \%$,what will be the uncertainty in its position?

Explain the graph of $\psi(r)$ and $\psi^2(r)$ with distance $r$ from the nucleus.

In an atom,an electron is moving with a speed of $600 \ m/sec$ with an uncertainty of $0.005\%$. The uncertainty with which the position of the electron can be located is:

The uncertainty in the position of an electron $(\Delta x)$ is approximately $100 \ pm$. Calculate the uncertainty in momentum $(\Delta p)$ of the electron in $kg \ m \ s^{-1}$. $[h = 6.626 \times 10^{-34} \ J \ s]$

Given below are two statements $:$
Statement $(I):$ It is impossible to specify simultaneously with arbitrary precision,both the linear momentum and the position of a particle.
Statement $(II) :$ If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron,then the uncertainty in the measurement of velocity is $\geq \sqrt{\frac{h}{4\pi}} \times \frac{1}{m}$ which simplifies to $\geq \frac{1}{2m} \sqrt{\frac{h}{\pi}}$. In the light of the above statements,choose the correct answer from the options given below $:$